# 4D Gaussian Splatting as a Learned Dynamical System

arXiv: https://arxiv.org/abs/2512.19648 · HTML: https://mlsanity.com/paper/2512.19648/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 29 of 29)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [Segment Any 3D Gaussians](https://mlsanity.com/paper/2312.00860/) (2023)
- [DynMF: Neural Motion Factorization for Real-time Dynamic View Synthesis with 3D Gaussian Splatting](https://mlsanity.com/paper/2312.00112/) (2023)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Motion-aware 3D Gaussian Splatting for Efficient Dynamic Scene Reconstruction](https://mlsanity.com/paper/2403.11447/) (2024)
- [ReCapture: Generative Video Camera Controls for User-Provided Videos using Masked Video Fine-Tuning](https://mlsanity.com/paper/2411.05003/) (2024)
- [MotionGS: Exploring Explicit Motion Guidance for Deformable 3D Gaussian Splatting](https://mlsanity.com/paper/2410.07707/) (2024)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [MEGA: Memory-Efficient 4D Gaussian Splatting for Dynamic Scenes](https://mlsanity.com/paper/2410.13613/) (2024)
- [DeformGS: Scene Flow in Highly Deformable Scenes for Deformable Object Manipulation](https://mlsanity.com/paper/2312.00583/) (2023)
- [Fluid Simulation on Neural Flow Maps](https://mlsanity.com/paper/2312.14635/) (2023)
- [CoMoGaussian: Continuous Motion-Aware Gaussian Splatting from Motion-Blurred Images](https://mlsanity.com/paper/2503.05332/) (2025)

## Built on by (most cited first, 4 of 4)

- [Envision4D: Envisioning Visual Futures via Feed-forward 4D Gaussian Splatting for Autonomous Driving](https://mlsanity.com/paper/2606.10656/) (2026)
- [GEM: Gaussian Evolution Model for Occupancy Forecasting and Motion Planning](https://mlsanity.com/paper/2605.17682/) (2026)
- [Future Rendering neq Future Surface: A Benchmark and Dataset for Dynamic Surface Reconstruction Beyond the Observed Window](https://mlsanity.com/paper/2607.21471/) (2026)
- [LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting](https://mlsanity.com/paper/2608.16324/) (2026)

## Abstract (arXiv)

We reinterpret 4D Gaussian Splatting as a continuous-time dynamical system, where scene motion arises from integrating a learned neural dynamical field rather than applying per-frame deformations. This formulation, which we call EvoGS, treats the Gaussian representation as an evolving physical system whose state evolves continuously under a learned motion law. This unlocks capabilities absent in deformation-based approaches:(1) sample-efficient learning from sparse temporal supervision by modeling the underlying motion law; (2) temporal extrapolation enabling forward and backward prediction beyond observed time ranges; and (3) compositional dynamics that allow localized dynamics injection for controllable scene synthesis. Experiments on dynamic scene benchmarks show that EvoGS achieves better motion coherence and temporal consistency compared to deformation-field baselines while maintaining real-time rendering